Question

f(x) = V22g(x) = 2x + 1Find (1) (2). Include any restrictions on the domain.A.(3) (x) =器 ¥0OB (1) (z) = 0,2OC. () (z) = 9,27-2OD. (1) (2) = 220

Answer 1

Given the functions:

$\begin{gathered} f(x)=\sqrt[3]{2x} \\ g(x)=2x+1 \end{gathered}$

then the quotient f/g is:

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}$

then, notice that the cubic root of 2x is always defined for any real number, then, the domain will be all real numbers except the value that makes 2x+1 = 0, then:

$\begin{gathered} 2x+1=0 \\ \Rightarrow2x=-1 \\ \Rightarrow x=-\frac{1}{2} \end{gathered}$

therefore, the domain is all real numbers except -1/2